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arXiv · 1210.2269

Gromov-Witten theory of tame Deligne-Mumford stacks in mixed characteristic

Flavia Poma
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Abstract

We define Gromov-Witten classes and invariants of smooth proper tame Deligne-Mumford stacks of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth proper tame Deligne-Mumford stack over a Dedekind domain, we prove that the invariants of fibers in different characteristics are the same. We show that genus zero Gromov-Witten invariants define a potential which satisfies the WDVV equation and we deduce from this a reconstruction theorem for genus zero Gromov-Witten invariants in arbitrary characteristic.

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Flavia Poma. 2013-02-06. Gromov-Witten theory of tame Deligne-Mumford stacks in mixed characteristic. https://arxiv.org/abs/1210.2269

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